We propose a method that uses the back propagation (BP) neural network algorithm to optimize the design of the multipump Raman fiber amplifier. We determine the optimal training model by examining the number of hidden layers in the multilayer BP neural network and the number of neural nodes contained in it. The model more accurately reflects the mapping relationship between the wavelength and output of the pump light and the Raman net gain distribution, instead of the traditional method of solving the Raman-coupled wave equation. The experimental results show that, using the trained BP neural network model to train new validation datasets, the studied Raman amplifier achieves the desired performance, and the maximum error between the target value and the predicted value does not exceed 0.3 dB. Compared with previous studies, this design scheme improves the accuracy of model calculation and the optimization efficiency of the Raman amplifier.